Question

Solve the equation and graph the solution(s), if possible. 9|4p + 2| + 8 = 35

Answer 1

Solving an equation means finding a value of a variable that make the equation true. This value is called the solution of the equation. A mathematical equation is just like a balanced equation. Both sides of the equation should be equal at all times. Whatever we do to one side, has to be done on the opposite side.


`9|4p + 2| + 8 = 35`


`9|4p+2|=35-8`
`Subtract \ 8 \ from \ both \ sides`


`9|4p+2|=27`


`|4p+2|= (27)/(9)`
`Divide \ both \ sides \ by \ 9`


`|4p+2|=3`


`Break \ down \ the \ problem \ into \ these \ 2 \ equations`


`4p+2=3`


`-(4p+2)=3`


`Solve \ the \ 1st \ equation: \ 4p+2=3`


`4p=3-2`
`Subtract \ 2 \ from \ both \ sides`


`4p=1`


`p= (1)/(4)`
`Divide \ both \ sides \ by \ 4`


`Solve \ the \ 2nd \ equation: \ -(4p+2)=3`


`-4p−2=3`
`Simplify \ brackets`


`-4p=3+2`
`Add \ 2 \ to \ both \ sides`


`-4p=5`


`p= -(5)/(4)`


`Collect \ all \ solutions`


`p= -(5)/(4)` ,
`p= (1)/(4)`